Akhtar S. Khan

Behavior of Berea sandstone under confining pressure part I: Yield and failure surfaces, and nonlinear elastic response

Abstract Results of a comprehensive experimental study of Berea sandstone involving uniaxial and triaxial compression experiments ( σ 1 > σ 2 = σ 3 ) are presented in terms of axial and circumferential strains versus axial stress, as well as the failure stress states for different confining pressure. Based on these results a failure surface and an initial yield surface have been proposed, and since the elastic response of Berea sandstone is nonlinear, a constitutive model is given in terms of the hypoelasticity theory. The shear and bulk moduli are found to depend on confining pressure and volume strain, respectively, and the equations for this variation with confining pressure and deformation are obtained.

Large deformation in polycrystalline copper under combined tension-torsion, loading, unloading and reloading or reverse loading: A study of two incremental theories of plasticity

Abstract Experimental data from combined tension-torsion of thin walled tubes of annealed polycrystalline copper subjected to various non-proportionate loading, unloading and reverse loading paths are presented. The measurements are compared with predicted values from classical incremental theory of plasticity in terms of true stress and true strain and a recently developed incremental theory of plasticity by Bell in terms of nominal stress and nominal strain. These experimental data reveal that the plastic strain produced by the various proportionate and non-proportionate loading, unloading and reverse loading paths are in better agreement with Bells incremental theory of plasticity as compared to classical incremental theory.

Finite plastic strain in annealed copper during non-proportional loading

Abstract In this paper it is shown that experimental results obtained for finite plastic strain produced by widely different non-proportional loading paths in annealed copper are in close accord with a recently developed incremental theory of finite strain plasticity. The measured strain components exceed 30%. Some attention also is given to the magnitude of the error introduced by a deformation theory approximation.

An experimental study of large finite plastic deformation in annealed 1100 aluminum during proportional and nonproportional biaxial compression

Abstract A new nonproportional biaxial compression experiment has been developed where a rectangular block first undergoes uniaxial compression and then, after finite deformation, it is subjected to large deformations (up to 45% strain) under biaxial compression. Experimental results on rectangular specimens of annealed 1100 aluminum subjected to uniaxial and biaxial compressive loadings are presented. The experiments include proportional and nonproportional loading paths. Stress and strain measures, directional changes of plastic strain increment, and existence of the von Mises equivalent stress-strain relation at large finite strains are discussed. Small volume changes were computed from the measured strains; however, density measurements after unloading indicate negligible change in density or volume. The classical Prandtl-Reuss equations are shown to predict acceptable results when the true or logarithmic strain loading paths are approximately proportional; however, many constitutive models can predict the experimental results during proportional loading paths. On the other hand, during sharp directional changes in loading paths, the predictions using Prandtl-Reuss equations in terms of deviatoric stress ratios and incremental strain ratios do not agree with experimental data for nonproportional loading paths, especially in the neighborhood of loading path change.

An experimental study of stress wave transmission at a metallic-rock interface and dynamic tensile failure of sandstone, limestone, and granite

Abstract An experimental technique is described for determination of dynamic tensile fracture strength of brittle solids. This technique has been used to determine the dynamic tensile fracture strength of several types of rock. The rocks studied were granite, limestone, and sandstone; the specimens were cored perpendicular to the bedding plane for these rocks. The quasi-static fracture strengths of the same solids were also determined for comparison with the dynamic strengths. The dynamic strengths have been found to be several times the quasi-static strengths, thus showing a strong dependence of fracture strength on strain rate.

A study of two incremental theories of plasticity through large deformation in polycrystalline copper

Abstract Experimental data from combined tension-torsion of thin-walled annealed poly-crystalline copper tubes are compared with Prandtl-Reuss classical incremental theory and Bells finite deformation incremental theory. In the experiment, the loads are prescribed and the loading paths include proportionate and nonproportionate tension and torsion. One of the main differences between the two theories is that the former is in terms of true stress and strain, whereas the latter is in nominal stress and nominal strain form. Also in one case, the equivalent stress and equivalent strain curves are approximated by a general power relation, whereas in the other case, the relation is parabolic. The results obtained in this investigation suggest that the finite deformation incremental theory in terms of nominal stress and nominal strain predicts the material behavior better than the classical incremental theory.

A three-dimensional finite element program to predict ultimate fracture failure load

Abstract A finite element computer program using an eight-noded three-dimensional isoparametric finite element is developed to predict the initiation and propagation of fracture, load-displacement history and failure load in elastoplastic structural systems subjected to monotonically increasing loads. Isotropie material is considered. The program is based on small deformation theory and uses an incremental loading technique to load the structure. The approach uses two types of piecewise linear approximations for the non-linear portion of the actual uniaxial stress-strain curve for the material: (i) the tangent modulus concept and (ii) the secant modulus concept. Either the St. Venant or von Mises yielding criteria can be used to predict yielding or fracture. Three different methods of calculating element principal stresses/strains are incorporated to apply the yield criterion. The energy at fracture is redistributed by using the ‘zero modulus unload-reload scheme’. Two different problems are solved using the developed program to demonstrate its capabilities and accuracy: (i) a center cracked panel and (ii) a tubular T-connection. The results obtained by the finite element analyses compare well with the available results from experimental tests on similar specimens.

A comparative study of the stress field around a reinforced and an unreinforced normal intersection of two cylindrical shells

Abstract The results of a comparative study of the effects of reinforcement on the stress fields in the critical intersection region of two normally intersecting cylindrical shells are presented. The results for in-plane and out-of-plane moments have been obtained experimentally by the use of electrical resistance foil gages, and numerically by the use of a three-dimensional finite element program. The finite element analysis also includes internal pressure loading. A comparison of results obtained by using a thin shell element with six degrees of freedom at each of the four nodes (three displacements and three rotations) and a three-dimensional element with three displacement degrees of freedom at each of the eight nodes, is also given.

Shear measurement using strain gages under large deformation and rotation

The measurement of shear strain under finite deformation and large rotation by using electrical-resistance metallic foil strain gages is studied both analytically and experimentally. Equations for calculating shear strain and axial and circumferential stretches are derived based on the kinematics of general tension-torsion deformation mode. These equations are applied to analyzing pure torsion experimental data. Comparison is made between results obtained with strain gages and a rotary transducer. It is shown that, in case of large rotation, one simple equation can be used to calculate the shear strain up to 30 percent with adequate accuracy.

A three-dimensional finite element program for prediction of crack initiation and growth

Abstract A three-dimensional finite element computer program is presented for the prediction of crack initiation and growth (especially stable crack growth). The program is based on element-oriented crack modeling and uses a standard eight-noded isoparametric solid element and a self-adjusted stress redistribution logic. A center cracked panel is studied using the present program. The numerical results obtained using this three-dimensional program are found to be close to the computational results of Miller et al . ( Comput. Struct . 7 , 315–326) using a two-dimensional plane stress program.